Elite universities are not instinctively biased against disadvantaged children but must do more to improve access, the UK’s education secretary has said.

In his first major speech on social mobility, Damian Hinds said there was a “very legitimate public interest” to ensure attempts to encourage children to attend the top higher education institutions reach “deep into the country” and to every group.

He said university was key to determining children’s future success and suggested there was “encouraging progress” on social mobility due to increased numbers of children from disadvantaged backgrounds attending them.

But Hinds said it was “not acceptable” that 18-year-old applicants from the most advantaged areas of the country were still nearly five-and-a-half times more likely to enter the most selective universities than their more disadvantaged peers.

The Office for Students has been asked to identify the best approaches for getting children from different backgrounds into university, including the most selective.

Hinds said more needed to be done at schools in the light of data that shows private schools were responsible for 7% of the school population but 40% of those who went to Oxbridge universities in 2016-17.

He added that private schools represented 14% of A-level students and 25% of students getting three or more A grades.

The cabinet minister later highlighted an “expectation and knowledge gap”, pointing to middle-class parents encouraging their children to choose “harder” subjects such as maths, history and Mandarin as a “signalling device” to universities and employers.

Hinds’ remarks came during a Resolution Foundation event in London, where he said universities were expected to spend £860m to “improve access and success for disadvantaged students”, adding that it needed to be spent well and the challenges faced need to be recognised.

“The latest statistics on destinations of sixth-form and college students show that disadvantaged white pupils are less likely to be studying in higher education the next year than disadvantaged pupils from any other ethnic group,” Hinds said.

“And even though disadvantaged black pupils are almost twice as likely to go to a top-third university as white disadvantaged pupils, they are both similarly underrepresented at the most selective universities, including the Russell Group.”

He also highlighted regional variations in England, noting that one in five disadvantaged pupils from London goes to a top-third university compared with one in 17 from the north-east.

Pressed later by reporters, Hinds said: “Do I think that elite universities are biased against disadvantaged children? No, I don’t think instinctively they are; I think they want people to be able to benefit from what they have to offer.

“But I think we need to go further, they need to go further. There’s a lot of money being spent on these access programmes and so on, and there’s a very legitimate public interest in making sure that absolutely reaches out as deep into the country and to every group as it can.”

A new big-data project will also be commissioned, based on work in the US, to look at young people from across the UK and where they end up in the next five or six years, the minister said.

He also addressed research showing communication skills such as being able to talk about events in the past or future were missing in 28% of four- and five-year-olds, and pledged to halve the number of children starting school without the early speaking and reading skills they need by 2028.

An education summit involving businesses and broadcasters this autumn will help find ways to encourage more parents to read and learn new words with their children.